The families, from South Ronaldsay, had sought compensation for trauma and distress caused by the removal of their children, who spent five weeks in council care. Last night the council and families issued a joint statement saying the civil actions had been settled out of court.
Each child and parent would receive damages and expenses, which would be paid by the council's insurers, with a contribution from the council - understood to be a sum not exceeding pounds 50,000.
The removal of the children followed allegations of sex abuse by two children already in care as a result of an earlier case in which abuse was established. The nine were reunited with their parents after five weeks in care. At a court hearing in Kirkwall, a sheriff threw out the case against the parents, saying it was fatally flawed.
Lord Clyde's judicial inquiry into the affair sat for 135 days and cost an estimated pounds 6m. He criticised social workers for acting hastily, without enough thought and after a poorly organised investigation into the sex- abuse allegations.
Orkney Islands Council said it fully accepted Lord Clyde's criticisms and asked all members of the four families to accept its "wholehearted" apology.
The council said it hoped the apology would mark a start in repairing the damage to the relationship between the local community and Orkney social- work department. A spokesman for the families, who were never named for legal reasons but became known by their initials E, H, M and T, refused to say how much they would receive.